When they are moving the eggs and/or golf balls around under them its not unusual for them to scratch one a bit with their toenails. I see it from time to time; got a scratched one today as a matter of fact.

Is the scratch an actual groove in the eggshell? Or more like the 'paint/coating' was scratched?

If it is the paint/coating looking scratched it could be because when the egg comes out of the hen, it can be a little sticky and moist - and if a strand of hay gets stuck to it, the coating might look scratched.

At least, that's what the scratches are on my eggs. (And my greedy thumbprints too on Saturday mornings!)

there are several scratches like it was done by a beak or maybe toenails. It is very odd. I don't have any hay there is pine shavings and some strips of newspaper in the nesting box--that all three of my layers use and ignore the other boxes.

Betcha it was just normal scratches. Nothing more than the outer layer (the "top coat") that was scratched? It happens. No worries. Pecking marks would tend to be more concentrated in one small area.
Have your own chickens long enough and you'll see all kinds of little egg quirks. Most are entirely normal.